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The density difference lattice hydrodynamic model with on-ramp is proposed. Stochastic and deterministic rules for the on-ramp flow entering into the main road are designed. Under the stochastic rule, various empirical spatiotemporal patterns can be well reproduced, such as the pinned localized cluster (PLC) and homogeneous synchronized traffic (HST). Under the deterministic rule, four new types of congested traffic states, such as the stationary oscillatory congested traffic (OCT) upstream of on-ramp and the stationary and localized OCT emerging in HST, are identified for the first time. Comparisons with the macroscopic speed gradient model are carried out, and some advantages of our model are clarified. To our knowledge, it is the first research showing that the lattice hydrodynamic model could reproduce various congested patterns induced by the on-ramp system

Dynamic Congested Traffic States of Density Difference Lattice Hydrodynamic Model with On-Ramp